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Stabilization-Free H(curl) and H(div)-Conforming Virtual Element Method

arXiv:2501.15168v2 Announce Type: replace Abstract: Standard Virtual Element Method (VEM) requires stabilization terms that significantly affect the numerical computation performance. In this work, we propose a stabilization-free VEM for general order \(\mathbf{H}(\operatorname{\mathbf{curl}})\) and \(\mathbf{H}(\operatorname{div})\)-conforming spaces by constructing novel serendipity projectors and corresponding serendipity spaces with minimum number of DoFs. Our approach handles the full...

arXiv CS 8d ago

A Mixed Extended Virtual Element Method for Elliptic Interface Problems on Polygonal Meshes

arXiv:2606.08526v1 Announce Type: new Abstract: We propose a lowest-order \(H(\operatorname{div})\)-conforming mixed extended virtual element method for elliptic interface problems on interface-unfitted polygonal meshes. The flux and pressure are approximated by subdomain-wise extended \(H(\operatorname{div})\)-VEM spaces and by piecewise constants, respectively. On cut elements, the computable polynomial projection is defined on the whole background element and then restricted to the two...

arXiv CS 1d ago

Discrete Incremental Voting: New Bounds for General Graphs and Expanders

arXiv:2606.06381v1 Announce Type: new Abstract: We analyze the discrete incremental voting process (DIV) introduced by Cooper, Radzik, and Shiraga [OPODIS '23]. In this process, we consider a set $V$ of $n$ nodes connected in an undirected graph $G = (V, E)$ where each node has an integer opinion. In one step a randomly selected node interacts with its randomly selected neighbor and changes its opinion by $1$ in the direction of the neighbour's opinion.

arXiv CS 5d ago

AutoNumerics-Zero: Automated Discovery of State-of-the-Art Mathematical Functions

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arXiv CS 6d ago

Divergence-free unfitted finite element discretisations for the Darcy problem

arXiv:2603.26212v2 Announce Type: replace Abstract: We develop an unfitted compatible finite element discretisation for the Darcy problem based on $H(\mathrm{div})$-conforming flux spaces and discontinuous pressure spaces. The method is designed to preserve pointwise discrete mass conservation while remaining robust in the presence of arbitrarily small cut cells arising from unfitted meshes. Robustness is achieved by combining an $L^2$-stabilisation of the flux with an additional mixed-term...

arXiv CS 2d ago

Volatility surge has trader eyeing one 'stable' stock

With semis whipping around on every AI headline and index volatility spiking, I'm looking for a counterpoint, a stable, cash-generating business where I can sell volatility instead of buying drama. Cigna (CI) fits the bill — and I'd rather write my way into the stock than chase it. Cigna isn't a growth story.

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Agentic Mfw

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Christen Goff hit the runway for Swim Week, Alysha Newman in Miami for the festivities & a dinger to the dome

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